%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET016+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:42:37 PM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 12 unt; 2 def)
% Number of atoms : 80 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 63 ( 25 ~; 23 |; 4 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 44 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(f8,axiom,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(f9,axiom,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( X0 = X1
| X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',unordered_pair) ).
fof(f12,conjecture,
! [X0,X1,X2,X3] :
( equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X2),unordered_pair(X2,X3)))
=> X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI50a) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X2),unordered_pair(X2,X3)))
=> X0 = X2 ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( equal_set(X0,X1)
=> ( subset(X0,X1)
& subset(X1,X0) ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
| ~ equal_set(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f18,plain,
? [X0,X1,X2,X3] :
( X0 != X2
& equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X2),unordered_pair(X2,X3))) ),
inference(ennf_transformation,[],[f13]) ).
fof(f19,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f22,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f36,plain,
! [X0,X1] :
( X0 != X1
| member(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f8]) ).
fof(f37,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f8]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[],[f9]) ).
fof(f40,plain,
! [X2,X0,X1] :
( X0 != X1
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f47,plain,
equal_set(unordered_pair(singleton(sK3),unordered_pair(sK3,sK4)),unordered_pair(singleton(sK5),unordered_pair(sK5,sK6))),
inference(cnf_transformation,[],[f18]) ).
fof(f48,plain,
sK3 != sK5,
inference(cnf_transformation,[],[f18]) ).
fof(f49,plain,
! [X1] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f36]) ).
fof(f50,plain,
! [X2,X1] : member(X1,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f40]) ).
fof(f52,plain,
subset(unordered_pair(singleton(sK5),unordered_pair(sK5,sK6)),unordered_pair(singleton(sK3),unordered_pair(sK3,sK4))),
inference(resolution,[],[f22,f47]) ).
fof(f60,plain,
! [X0] :
( ~ member(X0,unordered_pair(singleton(sK5),unordered_pair(sK5,sK6)))
| member(X0,unordered_pair(singleton(sK3),unordered_pair(sK3,sK4))) ),
inference(resolution,[],[f19,f52]) ).
fof(f65,plain,
member(singleton(sK5),unordered_pair(singleton(sK3),unordered_pair(sK3,sK4))),
inference(resolution,[],[f60,f50]) ).
fof(f196,plain,
( singleton(sK3) = singleton(sK5)
| unordered_pair(sK3,sK4) = singleton(sK5) ),
inference(resolution,[],[f38,f65]) ).
fof(f211,definition,
( spl7_5
<=> unordered_pair(sK3,sK4) = singleton(sK5) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
fof(f213,plain,
( unordered_pair(sK3,sK4) = singleton(sK5)
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f215,definition,
( spl7_6
<=> singleton(sK3) = singleton(sK5) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
fof(f217,plain,
( singleton(sK3) = singleton(sK5)
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f218,plain,
( spl7_5
| spl7_6 ),
inference(avatar_split_clause,[],[f196,f215,f211]) ).
fof(f233,plain,
( member(sK3,singleton(sK5))
| ~ spl7_5 ),
inference(superposition,[],[f50,f213]) ).
fof(f327,plain,
( sK3 = sK5
| ~ spl7_5 ),
inference(resolution,[],[f233,f37]) ).
fof(f328,plain,
( $false
| ~ spl7_5 ),
inference(forward_subsumption_resolution,[],[f327,f48]) ).
fof(f329,plain,
~ spl7_5,
inference(avatar_contradiction_clause,[],[f328]) ).
fof(f354,plain,
( member(sK5,singleton(sK3))
| ~ spl7_6 ),
inference(superposition,[],[f49,f217]) ).
fof(f369,plain,
( sK3 = sK5
| ~ spl7_6 ),
inference(resolution,[],[f354,f37]) ).
fof(f370,plain,
( $false
| ~ spl7_6 ),
inference(forward_subsumption_resolution,[],[f369,f48]) ).
fof(f371,plain,
~ spl7_6,
inference(avatar_contradiction_clause,[],[f370]) ).
cnf(s3,plain,
( spl7_5
| spl7_6 ),
inference(sat_conversion,[],[f218]) ).
cnf(s4,plain,
~ spl7_5,
inference(sat_conversion,[],[f329]) ).
cnf(s5,plain,
~ spl7_6,
inference(sat_conversion,[],[f371]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s3,s5,s4]) ).
fof(f372,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET016+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n016.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Mon Sep 28 00:12:03 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.43 Running first-order model finding
% 0.11/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.48 % (3140895)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (3140904)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=23767354:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (3140901)% WARNING: option uhcvi not known.
% 0.17/0.48 % (3140904) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3140895-3140904"...
% 0.17/0.48 % (3140904)...printing done.
% 0.17/0.48 % (3140900)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1522743008_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (3140901)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3406294932:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (3140906)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3913087341:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % (3140903)dis+10_1_sil=32000:sp=arity:random_seed=2655917314:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (3140904)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (3140904)------------------------------
% 0.17/0.48 % (3140904)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (3140904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (3140904)CaDiCaL version: 2.1.3
% 0.17/0.48 % (3140904)Termination reason: Refutation
% 0.17/0.48 % (3140904)Time elapsed: 0.006 s
% 0.17/0.48 % (3140904)Peak memory usage: 12 MB
% 0.17/0.48 % (3140904)Instructions burned: 15 (million)
% 0.17/0.48 % (3140895)Success in time 0.042 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------